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Sum

Find the value of x for which DE || AB in figure.

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#### Solution

DE || AB

Using basic proportionality theorem,

`(CD)/(AD) = (CE)/(BE)`

∴ If a line is drawn parallel to one side of a triangle such that it intersects the other sides at distinct points, then, the other two sides are divided in the same ratio.

Hence, we can conclude that, the line drawn is equal to the third side of the triangle.

⇒ `(x + 3)/(3x + 19) = x/(3x + 4)`

(x + 3) (3x + 4) = x (3x + 19)

3x^{2} + 4x + 9x + 12 = 3x^{2} + 19x

19x – 13x = 12

6x = 12

∴ x = `12/6` = 2

Concept: Basic Proportionality Theorem (Thales Theorem)

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